Related papers: Redundancy in Logic II: 2CNF and Horn Propositiona…
The sophisticated structure of Convolutional Neural Network (CNN) allows for outstanding performance, but at the cost of intensive computation. As significant redundancies inevitably present in such a structure, many works have been…
Given the emergent reasoning abilities of large language models, information retrieval is becoming more complex. Rather than just retrieve a document, modern information retrieval systems advertise that they can synthesize an answer based…
The presence of second-order smoothness for objective functions of optimization problems can provide valuable information about their stability properties and help us design efficient numerical algorithms for solving these problems. Such…
Over the past few decades, non-monotonic reasoning has developed to be one of the most important topics in computational logic and artificial intelligence. Different ways to introduce non-monotonic aspects to classical logic have been…
Tree-structured recursive neural networks (TreeRNNs) for sentence meaning have been successful for many applications, but it remains an open question whether the fixed-length representations that they learn can support tasks as demanding as…
We present a simpler way than usual to deduce the completeness theorem for the second-oder classical logic from the first-order one. We also extend our method to the case of second-order intuitionistic logic.
It is well-known that biological and social interaction networks have a varying degree of redundancy, though a consensus of the precise cause of this is so far lacking. In this paper, we introduce a topological redundancy measure for…
A new syntactic characterization of problems complete via Turing reductions is presented. General canonical forms are developed in order to define such problems. One of these forms allows us to define complete problems on ordered…
We verify a confluence result for the rewriting calculus of the linear category introduced in our previous paper. Together with the termination result proved therein, the generalized coherence theorem for linear category is established.…
Circular (or cyclic) proofs have received increasing attention in recent years, and have been proposed as an alternative setting for studying (co)inductive reasoning. In particular, now several type systems based on circular reasoning have…
This is a survey on propositional proof complexity aimed at introducing the basics of the field with a particular focus on a method known as feasible interpolation. This method is used to construct "hard theorems" for several proof systems…
We consider approximating data structures with collections of the items that they contain. For examples, lists, binary trees, tuples, etc, can be approximated by sets or multisets of the items within them. Such approximations can be used to…
Hybrid logic with binders is an expressive specification language. Its satisfiability problem is undecidable in general. If frames are restricted to N or general linear orders, then satisfiability is known to be decidable, but of…
We revisit the classical theory of linear second-order uniformly elliptic equations in divergence form whose solutions have H\"older continuous gradients, and prove versions of the generalized maximum principle, the $C^{1,\alpha}$-estimate,…
Recurrent neural networks (RNNs) have achieved state-of-the-art performances in many natural language processing tasks, such as language modeling and machine translation. However, when the vocabulary is large, the RNN model will become very…
Complex classifiers may exhibit "embarassing" failures in cases where humans can easily provide a justified classification. Avoiding such failures is obviously of key importance. In this work, we focus on one such setting, where a label is…
We consider two decision problems for linear recurrence sequences (LRS) over the integers, namely the Positivity Problem (are all terms of a given LRS positive?) and the Ultimate Positivity Problem} (are all but finitely many terms of a…
The satisfiability problem of hybrid logics with the downarrow binder is known to be undecidable. This initiated a research program on decidable and tractable fragments. In this paper, we investigate the effect of restricting the…
The objective of this paper is to improve the customary definition of redundancy by providing quantitative measures in its place, which we coin upper and lower redundancies, that match better with an intuitive understanding of redundancy…
The origin of complex structures, randomness, and irreversibility are analyzed in the scale free SL(2,R) analysis, which is an extension of the ordinary analysis based on the recently uncovered scale free $C^{2^n-1}$ solutions to linear…